Stop without aspiration to publicise star (6)
I believe the answer is:
altair
'star' is the definition.
(Altair is a star in the constellation of Aquila)
'stop without aspiration to publicise' is the wordplay.
'stop' becomes 'halt' (halt can mean to stop).
'without' is a deletion indicator.
'aspiration' becomes 'h' (speech sound from a puff of breath).
'to publicise' becomes 'air' ('air' can be a synonym of 'publicise').
'halt' with 'h' removed is 'alt'.
'alt'+'air'='ALTAIR'
(Other definitions for altair that I've seen before include "Heavenly body" , "Member of Eagle family" , "Bright star in Aquila" , "First-magnitude star" , "Bright star; lariat (anag.)" .)